Climate change is a growing threat to cultural heritage buildings and objects. Objects housed in historic buildings are at risk because the indoor environments in these buildings are difficult to control and often influenced by the outdoor climate. Hygroscopic materials, such as wood, will gain and release moisture during changes in relative humidity and temperature. These changes cause swelling and shrinkage, which may result in permanent damage. To increase the knowledge of climate-induced damage to heritage objects, it is essential to monitor moisture transport in wood. Simulation models need to be developed and improved to predict the influence of climate change. In a previous work, relative humidity and temperature was monitored at different depths inside wooden samples subjected to fluctuating climate over time. In this article, two methods, the hygrothermal building simulation software WUFI® Pro and the Simplified model, were compared in relation to the measured data. The conclusion was that both methods can simulate moisture diffusion and transport in wooden object with a sufficient accuracy. Using the two methods for predicted climate change data show that the mean RH inside wood is rather constant, but the RH minimum and maximum vary with the predicted scenario and the type of building used for the simulation.